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Re: [PrimeNumbers] Erroneous Information

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  • Phil Carmody
    ... My mail receiving operation M could be nilpotent. Or maybe M is idempotent. Perhaps neither of the above. If so, and M^2 == I... ... You should see my
    Message 1 of 8 , Mar 5, 2001
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      On Mon, 05 March 2001, Chris Harrison wrote:
      > Dear All,
      >
      > Please be aware that I have e-mailed Phil Carmody TWICE to ask him to
      > correct his assertion copied below:

      My mail receiving operation M could be nilpotent.
      Or maybe M is idempotent.
      Perhaps neither of the above. If so, and M^2 == I...

      > >On Sun, 04 March 2001, "�� ����" wrote:
      > > who can give me a twin primes table below 1024 bits,or an address, thank you!
      >
      > >on't be fooled by the name, these only go up to 15 digits:
      > >http://www.meganumbers.com/
      >
      > >If you want anything larger, your best bet is to generate them yourself.
      >
      > and he has not responded, hence this e-mail.

      You should see my inbox! One tediously long meeting and lunch - that's all it takes.
      At least we know the primenumbers list is "active" now!

      > There are IN FACT bulk sequences of primes up to 19 digits in length
      > at the MegaNumberS web site.

      My mistake, sorry. However, as has been noted elsewhere, 10^19 is still "small" compared to the ~1000 bit range being mentioned. I'd not actually perused the 'meganumbers' site before, so wasn't previously aware of what it contained. However, as this side of the globe was awake, and the Americans were probably asleep, I thought that I'd do the "run around the primepages finding pointers" job. It's only those that actually do things that get criticised, so I don't feel too bad at having one bogus character in my entire reply.

      Phil




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    • Jud McCranie
      At 11:45 AM 3/5/2001 +0000, Chris Harrison wrote: There are IN FACT bulk sequences of primes up to 19 digits in length ... I ve got a list up to 2^32, which is
      Message 2 of 8 , Mar 5, 2001
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        At 11:45 AM 3/5/2001 +0000, Chris Harrison wrote:
        There are IN FACT bulk sequences of primes up to 19 digits in length
        >at the MegaNumberS web site.

        I've got a list up to 2^32, which is about 19 digits, but that is a long
        way from the requested 2^1024.

        +--------------------------------------------------------+
        | Jud McCranie |
        | |
        | 137*2^261147+1 is prime! (78,616 digits, 5/2/00) |
        +--------------------------------------------------------+
      • Jud McCranie
        ... I keep my list up to 2^32 on disk, even though I think it would be faster to generate them. (At some point it becomes slower to generate them.) The
        Message 3 of 8 , Mar 5, 2001
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          At 07:47 AM 3/5/2001 -0500, Jack Brennen wrote:

          > "The problem with answering this question is small primes are too
          > easy to find. The can be found far faster than they can be read from
          > a hard disk, so no one bothers to keep long lists (say past 10^9).
          > Long lists just waste storage, and on the Internet, they just waste
          > bandwidth."

          I keep my list up to 2^32 on disk, even though I think it would be faster
          to generate them. (At some point it becomes slower to generate them.) The
          reason I do that rather than generate them each time is for
          reliability. If I'm looking at primes of a certain type, I read them in
          and check. I think this is saver than changing the generating program each
          time. Also the program to read them in is a lot shorter and less prone to
          error than the generating program.

          +--------------------------------------------------------+
          | Jud McCranie |
          | |
          | 137*2^261147+1 is prime! (78,616 digits, 5/2/00) |
          +--------------------------------------------------------+
        • Ben Bradley
          ... I ve got something similar on my website - a short description of primes, with C source to programs to generate and read primes in a successive-differences
          Message 4 of 8 , Mar 5, 2001
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            At 11:50 AM 3/5/01 -0500, Jud McCranie wrote:
            >At 07:47 AM 3/5/2001 -0500, Jack Brennen wrote:
            >
            >> "The problem with answering this question is small primes are too
            >> easy to find. The can be found far faster than they can be read from
            >> a hard disk, so no one bothers to keep long lists (say past 10^9).
            >> Long lists just waste storage, and on the Internet, they just waste
            >> bandwidth."
            >
            >I keep my list up to 2^32 on disk, even though I think it would be faster
            >to generate them. (At some point it becomes slower to generate them.) The
            >reason I do that rather than generate them each time is for
            >reliability. If I'm looking at primes of a certain type, I read them in
            >and check. I think this is saver than changing the generating program each
            >time. Also the program to read them in is a lot shorter and less prone to
            >error than the generating program.

            I've got something similar on my website - a short description of
            primes, with C source to programs to generate and read primes in a
            successive-differences format. My format uses four bits to store the
            difference between the majority of primes under 2^32 (and multiples of
            four bits for the rest). For this range, the file format takes an average
            of about (I forget the exact numbers) five bits per prime.
            I heard and read several places that it's faster to generate primes
            in RAM with a sieve than to read them from a file, which I never
            understood, because my programs read the disk format and recreate
            the primes in about half the time it takes to generate them in RAM.
            One caveat, the programs don't work well with numbers near 2^32. :(
            -----
            This post (except quoted portions) Copyright 2001, Ben Bradley.
            http://listen.to/benbradley
          • Jud McCranie
            At 03:16 PM 3/5/2001 -0500, Ben Bradley wrote: I heard and read several places that it s faster to generate primes ... It is up to a point, and that point
            Message 5 of 8 , Mar 5, 2001
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              At 03:16 PM 3/5/2001 -0500, Ben Bradley wrote:
              I heard and read several places that it's faster to generate primes
              >in RAM with a sieve than to read them from a file,


              It is up to a point, and that point depends on the speed of your CPU and
              disk drive. Reading from the file is pretty much linear in the number of
              primes, which is sub-linear for primes below a limit, whereas a sieve is
              super-linear, so for large enough numbers, the sieve will take longer. On
              my machine, reading primes < 2^32 from disk is about twice as fast as my sieve.


              +--------------------------------------------------------+
              | Jud McCranie |
              | |
              | 137*2^261147+1 is prime! (78,616 digits, 5/2/00) |
              +--------------------------------------------------------+
            • Phil Carmody
              A carefully constructed dump of a sieve will beat most run-length compression schemes, even with huffman (or other entropy) compresion. For broad ranges, I d
              Message 6 of 8 , Mar 5, 2001
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                A carefully constructed dump of a sieve will beat most run-length compression schemes, even with huffman (or other entropy) compresion.
                For broad ranges, I'd use a 480/2310 comb to the sieve.
                For small ranges (a million primes) a 8/30 comb is fine.
                With the right code, I guestimate that generating primes should be faster than reading them off disk still, but it's not by a huge margin. Race Dan Bernstein's Primegen and Eratspeed against your hard disk for primes up to a billion if you don't believe me. (there are links on the primepages)

                However, my current sieving job is generating 17 digit numbers, and I store the deltas, which average around 7-8 digits. This gives me roughly 2:1 compression. I then BZIP2 them, which gives an almost exact log(10)/log(256) ratio, as the numbers are essentially unpredictable. Even then, I think I could fill a CD in a month.

                Twins fall into this latter catagory, and their density means that hard disk storage is worthwhile.

                Phil

                Mathematics should not have to involve martyrdom;
                Support Eric Weisstein, see http://mathworld.wolfram.com
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